WASHINGTON — The plan was straightforward: After years of being challenged by President Trump and others about a decades-old claim of Native American ancestry, Senator Elizabeth Warren of Massachusetts would take a DNA test to prove her stated family origins in the Cherokee and Delaware tribes.

But nearly two months after Ms. Warren released the test results and drew hostile reactions from prominent tribal leaders, the lingering cloud over her likely presidential campaign has only darkened. Conservatives have continued to ridicule her. More worrisome to supporters of Ms. Warren’s presidential ambitions, she has yet to allay criticism from grass-roots progressive groups, liberal political operatives and other potential 2020 allies who complain that she put too much emphasis on the controversial field of racial science — and, in doing so, played into Mr. Trump’s hands.

Advisers close to Ms. Warren say she has privately expressed concern that she may have damaged her relationships to Native American groups and her own standing with activists, particularly those who are racial minorities. Several outside advisers are even more worried: They say they believe a plan should be made to repair that damage, possibly including a strong statement of apology.

The advisers say Ms. Warren will have to confront the issue again if she announces a presidential campaign, which is expected in the coming weeks, and several would like her to act soon.

Publicly, at this point, the senator isn’t second-guessing her actions.

“There have been a lot of thoughtful conversations about this, and I appreciate that,” Ms. Warren said in an interview. “I believe for everyone in public life that transparency is crucial.”

Asked if the criticism of the test has inspired any regret, Ms. Warren said: “I put it out there. It’s on the internet for anybody to see. People can make of it what they will. I’m going to continue fighting on the issues that brought me to Washington.”

For some Warren allies and progressive groups, Ms. Warren’s standing by the DNA test amounts to profoundly poor judgment. Some said she was too reactive to Mr. Trump’s attacks — test results would never silence a president who often disregards facts, they said — and created a distraction from her own trademark message of economic populism. The president revels in repeatedly slurring Ms. Warren as “Pocahontas,” and conservative commentators like Howie Carr of The Boston Herald have enjoyed holding the DNA issue over the senator’s head.

“The biggest risk in engaging a bully is that bullies don’t usually stop, regardless of what the truth is,” said Charles Chamberlain, executive director for the progressive political group Democracy for America. Mr. Chamberlain’s group had, in 2014, launched a “Run Warren Run” campaign to encourage her to seek the 2016 presidential nomination.

“When you can’t win an argument,” he added, “then sometimes it’s not worth having that argument.”

Ms. Warren’s allies also say she unintentionally made a bigger mistake in treading too far into the fraught area of racial science — a field that has, at times, been used to justify the subjugation of racial minorities and Native Americans.

Ms. Warren has also troubled advocates of racial equality and justice, who say her attempt to document ethnicity with a DNA test gave validity to the idea that race is determined by blood — a bedrock principle for white supremacists and others who believe in racial hierarchies. Native American critics, including Kim TallBear, a prominent scholar from the University of Alberta, said in October that Ms. Warren’s actions relied on “settler-colonial” definitions of who is an indigenous American and amounted to a haughty refusal to hear out her longstanding critics.

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Cut-outs of Ms. Warren wearing a feathered headdress and Shiva Ayyadurai, her independent opponent in her re-election race, at the Conservative Political Action Conference in February.CreditChip Somodevilla/Getty Images

This line of criticism has particularly stung Ms. Warren, who has made a point to hold several private talks with Native leaders since taking the DNA test, emphasizing her respect for tribal sovereignty and making clear she does not claim tribal citizenship.

Three people close to senior members of Ms. Warren’s team, who were granted anonymity to speak freely on the issue, said they were “shocked” and “rattled” by the senator’s decision to take the DNA test, which they described as an unequivocal misstep that could have lasting consequences, even on 2020 staffing. One former adviser, who also asked not to be named, called it a “strategic failure” that was “depressing and unforgettable.”

Jennifer Epps-Addison, co-director for the Center for Popular Democracy, a group that has previously been supportive of Ms. Warren, said, “If she wants to be considered the leader of our party or the leader of the progressive movement, she needs a reconciliation.”

“And that reconciliation should center Native voices and make sure that their stories of loss and theft of identity come front and center, not, you know, one white woman’s tale of understanding her DNA,” Ms. Epps-Addison said.

Ms. Warren’s claim to Native American heritage first became an issue in her 2012 race for Senate, when The Herald reported that Harvard had once identified her as a member of a minority group when she was a law professor there. The Warren campaign at the time also confirmed she had listed herself as a minority member in a legal directory, but said she had done nothing wrong and said Native American ancestry had been part of her “family lore.” Her Republican opponent that year, Scott Brown, seized on the disclosures; she ultimately won the race by seven percentage points, but Republicans like Mr. Trump have continued to accuse her of misrepresenting herself for years.

The new chapter marks unfamiliar territory for Ms. Warren, who has rarely, if ever, been so vocally criticized by leaders and activists on the left. Some white progressives have stumbled on issues of race and identity, but before the DNA test was released, Ms. Warren had built a reservoir of good will among liberals on these issues. She received praise for lending her national platform to highlighting injustice against Native Americans recently and, in one high-profile incident, she impressed social justice activists when she refused to backtrack after calling the American criminal justice system “racist” from “front to back.”

Few think that this good will has completely disappeared, but the last month has seen even individuals who had previously been bullish on Ms. Warren’s potential candidacy reconsider their position. The questioning comes from a place of disappointment, because many of Ms. Warren’s backers believe she is better on issues of racial justice and identity than her handling of this issue may imply.

“Democratic candidates have a long history of not striking back fast enough when it comes to false narratives against them,” said Rebecca Katz, the New York-based progressive strategist. “Warren should get some credit for trying and pushing back hard, but we all have to be wide-eyed when it comes to race.”

“Our 2020 candidates need to understand race and identity in a way that tripped up candidates in 2016,” she said.

Progressive groups also lament that Ms. Warren kept the decision to take the test so closely guarded. Several said that if a greater diversity of stakeholders had been included in the conversation, including people whom Ms. Warren often consults during policy rollouts, much of the current fallout could have been avoided.

In interviews, several left-leaning groups wondered if Ms. Warren’s decision to take the DNA test was indicative of a larger problem for several prospective presidential candidates: that their inner circles of advisers don’t reflect the racial diversity of the Democratic electorate.

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Ms. Warren would begin among the front-runners for the Democratic presidential nomination if she chooses to run.CreditT.J. Kirkpatrick for The New York Times

“Race is a true third rail in American politics, and you can make a lot of mistakes when we don’t have a diverse set of folks who are in the room and empowered to make decisions,” said Eric Lundy, program director of Inclusv, a group that pushes for more diversity in political campaign staffs.

But as Ms. Warren inches closer to a presidential run, even critics of her decision to take the DNA test believe she is well positioned to shore up support. In the past week she has received heaps of praise for a foreign policy speech at American University, and she remains one of the party’s top fund-raisers and surrogates.

Allies in Boston pointed out that, in Ms. Warren’s recent re-election effort in Massachusetts, there was no evidence that the DNA announcement hurt her standing among voters. Those close to Ms. Warren also note they had several allies in the progressive and Native American communities who supported their decision from the outset.

Deb Haaland, the newly elected House member from New Mexico who will be one of the first Native American women to serve in Congress, said she believed the senator was seeking to learn more about her past. Other tribal leaders, including those from the Lenape Indian Tribe in Delaware and the Eastern Band of Cherokee in North Carolina, have also supported Ms. Warren’s decision. Ms. Warren’s DNA test, which was conducted by the renowned geneticist Carlos Bustamante and released by her office, showed strong evidence that Ms. Warren has Native American pedigree “6-10 generations ago.”

“I absolutely respect tribes’ authority to determine who are tribal members,” Ms. Haaland said. “But I don’t think that’s what Elizabeth Warren was doing. She was merely looking to find a connection to her past and that’s exactly what she did.”

This is not a view universally shared. The Cherokee Nation declined repeated requests for comment, but in a previous statement, tribal leaders said Ms. Warren’s decision dishonored “legitimate tribal governments and their citizens, whose ancestors are well documented and whose heritage is proven.”

Ian Haney López, the law and racial justice professor at the University of California, Berkeley, said Ms. Warren made a “naïve” error by not seeming to grasp the attack strategy of conservatives. Just as Mr. Trump used his so-called “birther” campaign to depict former President Barack Obama as a foreign-born immigrant, Mr. Trump was not seeking to make a factual claim against Ms. Warren but to brand her as an outsider, Mr. López said.

Twila Barnes, a Cherokee genealogist who has thoroughly tracked Ms. Warren’s claims of native ancestry since it became national news in 2012, said her “jaw was on the floor” when she saw Ms. Warren’s decision to take the DNA test, and the slick video that accompanied the announcement of the results.

Ms. Barnes said Ms. Warren had an opportunity to teach the broader public about how genetic testing has historically been used as a weapon against Native communities, but instead she “helped perpetuate a very dangerous idea.”

It has pushed Ms. Barnes, a self-described liberal, to make something of a personal pledge: She will never vote for Ms. Warren under any circumstance, including in an election against Mr. Trump.

Not even an apology — at this point — would help.

“She’s had six years to apologize,” she said.

Correction:

An earlier version of this article misspelled the surname of the executive director for Democracy for America. He is Charles Chamberlain, not Chamberlin.

Correction:

An earlier caption misidentified Ms. Warren’s Republican opponent in the 2018 Senate race. He was Geoff Diehl, not Shiva Ayyadurai, an independent candidate.

A version of this article appears in print on , on Page A1 of the New York edition with the headline: Warren Facing Cloud of Anger Over DNA Test. Order Reprints | Today’s Paper | Subscribe